Vibratory transducer

ABSTRACT

To conduct a fluid, the transducer has a flow tube which in use is vibrated by an excitation system and whose inlet-side and outlet-side vibrations are detected by means of a sensor system. In response to transverse forces produced in the vibrating flow tube, the latter is, at least temporarily, laterally displaced from an assigned static rest position. To improve the dynamic balance of the transducer, a first cantilever and a second cantilever are rigidly fixed to an inlet-side tube section and an outlet-side tube section, respectively. By means of the cantilevers, the inlet-side and outlet-side tube sections are deformed as a result of lateral displacements of the flow tube. This produces counterforces which at least partially counterbalance the transverse forces produced in the vibrating flow tube. One advantage of the proposed transducer is that it is well balanced even during variations in fluid density.

FIELD OF THE INVENTION

[0001] This invention relates to a vibratory transducer which isparticularly suited for use in a Coriolis mass flowmeter.

BACKGROUND OF THE INVENTION

[0002] To determine the mass flow rate of a fluid flowing in a pipe andparticularly of a liquid, use is frequently made of measuring deviceswhich induce Coriolis forces in the fluid and derive therefrom ameasurement signal representative of mass flow rate by means of avibratory transducer and of control and evaluation electronics connectedthereto.

[0003] Such Coriolis mass flowmeters have been known and in industrialuse for a long time. EP-A 317 340, U.S. Pat. Nos. 5,398,554, 5,476,013,5,531,126, 5,691,485, 5,705,754, 5,796,012, 5,945,609, and 5,979,246 aswell as WO-A 99/51946, WO-A 99/40349, and WO-A 00/14485, for example,disclose Coriolis mass flowmeters with a vibratory transducer whichresponds to the mass flow rate of a fluid flowing in a pipe andcomprises:

[0004] a single straight flow tube for conducting the fluid whichvibrates in operation and communicates with the pipe via an inlet-sidetube section and an outlet-side tube section;

[0005] an excitation system which in operation excites the flow tubeinto flexural vibrations in one tube plane; and

[0006] a sensor system for sensing inlet-side and outlet-side vibrationsof the flow tube.

[0007] As is well known, straight flow tubes excited into flexuralvibrations according to a first form of natural vibrations causeCoriolis forces in the fluid passing therethrough. These, in turn,result in higher-order and/or lower-order coplanar flexural vibrationsaccording to a second form of natural vibrations being superimposed onthe excited flexural vibrations, so that the vibrations sensed on theinlet and outlet sides by means of the sensor system exhibit ameasurable phase difference, which is also dependent on mass flow rate.

[0008] Usually, the flow tubes of such transducers, which are used inCoriolis mass flowmeters, for example, are excited in operation at aninstantaneous resonance frequency of the first form of naturalvibrations, particularly with the vibration amplitude maintainedconstant. Since this resonance frequency is also dependent on theinstantaneous density of the fluid in particular, commercially availableCoriolis mass flowmeters can also be used to measure the density ofmoving fluids.

[0009] One advantage of straight flow tubes is that they can be drainedresidue-free with a high degree of reliability in virtually any positionof installation and particularly after a cleaning operation performedin-line. Furthermore, such flow tubes are much easier and, consequently,less expensive to manufacture than, for example, an omega-shaped orhelically bent flow tube. A further advantage of a straight flow tubevibrating in the above-described manner over bent flow tubes is that inoperation, virtually no torsional vibrations are caused in the connectedpipe via the flow tube.

[0010] A significant disadvantage of such transducers consists in thefact that as a result of alternating lateral deflections of thevibrating single flow tube, transverse forces oscillating at the samefrequency can act on the pipe, and that so far it has been possible tocounterbalance these transverse forces only in a very limited manner andwith a very large amount of technical complexity.

[0011] To improve the dynamic balance of the transducer and particularlyreduce such transverse forces produced by the vibrating single flow tubeand acting on the pipe on the inlet and outlet sides, the transducersdisclosed in EP-A 317 340, U.S. Pat. Nos. 5,398,554, 5,531,126,5,691,485, 5,796,012, and 5,979,246 as well as WO-A 00/14485 eachcomprise at least one single-part or multipart “antivibrator” which isfixed to the flow tube on the inlet and outlet sides. In operation, suchantivibrators, which are implemented in the form of beams andparticularly of tubes or as a physical pendulum aligned with the flowtube, vibrate out of phase with, particularly opposite in phase to, therespective flow tube, whereby the effect of the lateral transverseforces exerted by the flow tube and the antivibrator on the pipe can beminimized or even neutralized.

[0012] Such transducers with antivibrators have proved particularlyeffective in applications where the fluid to be measured has asubstantially constant or only very slightly varying density, i.e., inapplications where a resultant of transverse forces produced by the flowtube and counterforces produced by the antivibrator, which resultantacts on the connected pipe, can be readily preset to zero.

[0013] If used for fluids with widely varying densities, such asdifferent fluids to be measured in succession, such a transducer,particularly one as disclosed in U.S. Pat. Nos. 5,531,126 or 5,969,265,has practically the same disadvantage, even though to a lesser degree,as a transducer without antivibrator, since the aforementionedresultants are also dependent on the density of the fluid and thus maydiffer considerably from zero. In other words, in operation, even anoverall system composed of flow tube and antivibrator will be nonlocallydeflected from an assigned static rest position as a result ofdensity-dependent unbalances and associated transverse forces.

[0014] One possibility of reducing the density-dependent transverseforces is proposed, for example, in U.S. Pat. No. 5,979,246, in WO-A99/40394, or in WO-A 00/14485. WO-A 00/14485, in particular, discloses avibratory transducer for a fluid flowing in a pipe, said transducercomprising:

[0015] a flow tube vibrating in operation, for conducting the fluid, theflow tube communicating with the pipe via an inlet-side tube section andan outlet-side tube section, and the vibrating flow tube being, at leasttemporarily, laterally displaced from an assigned static rest positionas a result of transverse forces produced therein, so that transverseimpulses occur in the transducer;

[0016] an excitation system for driving the flow tube;

[0017] a sensor system for sensing vibrations of the flow tube; and

[0018] a first antivibrator, fixed to the inlet-side tube section, and asecond antivibrator, fixed to the outlet-side tube section, forproducing compensating vibrations, the compensating vibrations beingsuch that the transverse impulses are compensated, so that a centroid ofa vibration system formed by the flow tube, the excitation system, thesensor system, and the two cantilevers is kept in the same position.

[0019] WO-A 99/40394 discloses a vibratory transducer for a fluidflowing in a pipe, said transducer comprising:

[0020] a flow tube vibrating in operation, for conducting the the fluid,the flow tube communicating with the pipe via an inlet-side tube sectionand an outlet-side tube section; and

[0021] an antivibrator fixed to the flow tube on the inlet side andoutlet side, with transverse forces being produced in the vibrating flowtube and in the antivibrator;

[0022] a transducer case fixed to the inlet-side tube section and theoutlet-side tube section;

[0023] an excitation system for driving the flow tube;

[0024] a sensing system for sensing vibrations of the flow tube;

[0025] a first cantilever, fixed to the inlet-side tube section and tothe transducer case, for producing counterforces counteracting thetransverse forces on the inlet side; and

[0026] a second cantilever, fixed to the outlet-side tube section and tothe transducer case, for producing counterforces counteracting thetransverse forces on the outlet side, the counterforces being such thatthe flow tube is held in an assigned static rest position despite thetransverse forces produced.

[0027] In the aforementioned transducers, including those described inU.S. Pat. No. 5,979,246, the problem of density-dependent unbalances issolved in principle by adapting an amplitude variation of theantivibrator to the flow-tube vibrations in advance and/or in operation,particularly by making the spring constants of the antivibratoramplitude-dependent, such that the forces produced by the flow tube andthe antivibrator neutralize each other.

[0028] Another possibility of reducing density-dependent transverseforces is described, for example, in U.S. Pat. Nos. 5,287,754,5,705,754, or 5,796,010. In the transducers disclosed therein, thetransverse forces produced by the vibrating single flow tube, whichoscillate at medium or high frequencies, are kept away from the pipe bymeans of an antivibrator that is very heavy in comparison with the flowtube, and by coupling the flow tube to the pipe relatively loosely,i.e., practically by means of a mechanical low-pass filter. A bigdisadvantage of such a transducer is, however, that the antivibratormass required to achieve sufficient damping increases disproportionatelywith the nominal diameter of the flow tube. Use of such massivecomponents, on the one hand, entails both increased assembly costsduring manufacture and increased costs during installation of themeasuring device in the pipe. On the other hand, it must always beensured that a minimum natural frequency of the transducer, whichdecreases with increasing mass, is still far from the likewise very lownatural frequencies of the connected pipe. Thus, use of such atransducer in industrial Coriolis mass flowmeters or Coriolis massflowmeter-densimeters and particularly in meters for measuring liquidsis limited to relatively small nominal diameters less than or equal to10 mm.

SUMMARY OF THE INVENTION

[0029] It is therefore an object of the invention to provide atransducer which is particularly suited for a Coriolis mass flowmeter ora Coriolis mass flowmeter-densimeter and which in operation, even if ituses only a single, particularly straight, flow tube, is dynamicallywell balanced over a wide fluid density range and nevertheless hascomparatively little mass.

[0030] To attain this object, the invention provides a vibratorytransducer for a fluid flowing in a pipe, said transducer comprising:

[0031] a flow tube vibrating in operation, for conducting the fluid, theflow tube communicating with the pipe via an inlet-side tube section andan outlet-side tube section, and the vibrating flow tube being, at leasttemporarily, laterally displaced from an assigned static rest positionas a result of transverse impulses occurring in the transducer;

[0032] an excitation system for driving the flow tube;

[0033] a sensor system for sensing vibrations of the flow tube;

[0034] a first cantilever, fixed to the inlet-side tube section, forcausing bending moments that elastically deform the inlet-side tubesection; and

[0035] a second cantilever, fixed to the outlet-side tube section, forcausing bending moments that elastically deform the outlet-side tubesection,

[0036] the bending moments being such that in the deforming inlet-sidetube section and in the deforming outlet-side tube section, impulses areproduced which are directed opposite to the transverse impulses producedin the vibrating flow tube.

[0037] Furthermore, the invention provides a vibratory transducer for afluid flowing in a pipe, said transducer comprising:

[0038] a flow tube vibrating operation, for conducting the fluid, theflow tube communicating with the pipe via an inlet-side tube section andan outlet-side tube section, and the vibrating flow tube being, at leasttemporarily, laterally displaced from an assigned rest position as aresult of transverse forces produced in the flow tube;

[0039] an excitation system for driving the flow tube;

[0040] a sensor system for sensing vibrations of the flow tube;

[0041] a first cantilever for causing bending moments that elasticallydeform the inlet-side tube section, said first cantilever having acantilever arm rigidly fixed to the inlet-side tube section and acantilever mass formed thereon;

[0042] a second cantilever for causing bending moments that elasticallydeform the outlet-side tube section, said second cantilever having acantilever arm rigidly fixed to the outlet-side tube section and acantilever mass formed thereon,

[0043] both the cantilever mass of the first cantilever and thecantilever mass of the second cantilever being spaced from the flowtube, from the inlet-side tube section, and from the outlet-side tubesection, and

[0044] the cantilever arm and cantilever mass of the first cantileverand the cantilever arm and cantilever mass of the second cantileverbeing so adapted to one another that a centroid of the first cantilever,located in the area of the inlet-side tube section, and a centroid ofthe second cantilever, located in the area of the outlet-side tubesection, remain essentially in a static rest position although the flowtube is laterally displaced from its assigned static rest position.

[0045] In a first preferred embodiment of the invention, the deforminginlet-side tube section and the deforming outlet-side tube section bendessentially in a direction opposite to that of the lateral displacementof the flow tube.

[0046] In a second preferred embodiment of the invention, the flow tubeis substantially straight.

[0047] In a third preferred embodiment of the invention, the vibratingflow tube performs flexural vibrations.

[0048] In a fourth preferred embodiment of the invention, each of thetwo cantilevers is at least as heavy as the flow tube.

[0049] In a fifth preferred embodiment of the invention, the transducercomprises an antivibrator fixed to the flow tube on the inlet and outletsides.

[0050] In a sixth preferred embodiment of the invention, theantivibrator is tubular in form.

[0051] In a seventh preferred embodiment of the invention, the flow tubeat least partly is enclosed by the antivibrator.

[0052] In an eighth preferred embodiment of the invention, the flow tubeand the antivibrator are coaxial.

[0053] In a ninth preferred embodiment of the invention, discrete masspieces are fixed to the antivibrator.

[0054] In a tenth preferred embodiment of the invention, grooves areformed in the antivibrator.

[0055] In an eleventh preferred embodiment of the invention, the masspieces fixed to the antivibrator are annular in shape and coaxial withthe antivibrator.

[0056] A fundamental idea of the invention is to convert lateraldisplacement motions of the vibrating flow tube, which tend to interferewith the measurements and/or have a disturbing effect on the connectedpipe and which are superimposed on the tube's primary deformations,i.e., on the deformations to be measured, into oppositely directeddeformations of the inlet-side and outlet-side tube sections thatdynamically balance the transducer.

[0057] One advantage of the invention is that, on the one hand, thetransducer is very well balanced despite possible operation-dependentvariations of the internal mass distribution, and thus alsoindependently of the density of the fluid, namely exclusively as aresult of its internal geometry forced by means of cantilevers, wherebyinternal transverse impulses and transverse forces can be largely keptaway from the connected pipe. On the other hand, the internaldeformation forces necessary therefor essentially do not act beyond thetransducer, particularly not on the pipe.

[0058] The transducer according to the invention is furthercharacterized by the fact that because of the dynamic vibrationisolation, it can be made very compact and very light. It turned outthat such a transducer can have more than 25% less mass than, forexample, a transducer whose internal transverse forces arecounterbalanced to a comparable extent by means of the above mentionedmechanical low-pass filter system. Therefore, the transducer isparticularly suited for measurements in pipes of great nominal diameter,e.g., greater than 80 mm.

BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The invention and further advantages will become more apparent byreference to the following description of an embodiment taken inconjunction with the accompanying drawings. Like reference charactershave been used to designate like parts throughout the various figures;reference characters that were already assigned are not repeated insubsequent figures if this contributes to clarity. In the drawings:

[0060]FIG. 1 is a partially sectioned side view of a Coriolis-typetransducer with one flow tube;

[0061]FIG. 2 is a partially sectioned side view of a development of thetransducer of FIG. 1;

[0062]FIGS. 3a show schematically deflection lines of the flow tubeduring to 3 d operation of the transducer of FIG. 1 or 2; and

[0063]FIG. 4 shows schematically a portion of the flow tube duringoperation of the transducer of FIG. 1 or 2.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

[0064] While the invention is susceptible to various modifications andalternative forms, exemplary embodiments thereof have been shown by wayof example in the drawings and will herein be described in detail. Itshould be understood, however, that there is no intent to limit theinvention to the the particular forms disclosed, but on the contrary,the intention is to cover all modifications, equivalents, andalternatives falling within the spirit and scope of the invention asdefined by the intended claims.

[0065]FIGS. 1 and 2 show a vibratory transducer in schematic side views.The transducer serves to produce in a fluid passing therethroughmechanical reaction forces, such as mass-flow-rate-dependent Coriolisforces, density-dependent inertial forces, and/or viscosity-dependentfriction forces, which react on the transducer and are measurable,particularly with sensor technology. From these reaction forces, a massflow rate m, a density ρ, and/or a viscosity η of the fluid, forexample, can thus be derived in the manner familiar to those skilled inthe art.

[0066] To conduct the fluid, the transducer comprises a substantiallystraight flow tube 10, particularly a single tube, which in operation,oscillating about a static rest position, is repeatedly elasticallydeformed.

[0067] To this end, flow tube 10 is mounted in a first support system 20so as to be capable of vibratory motion, the support system 20 beingfixed to flow tube 10 at the inlet and outlet ends. For the supportsystem 20, a supporting frame or a supporting tube can be used, forexample. Further preferred embodiments of support system 20 areexplained below.

[0068] To permit flow of fluid through flow tube 10, the latter isconnected to a fluid-conducting pipe via an inlet-side tube section 11and an outlet-side tube section 12. Flow tube 10, inlet-side tubesection 11, and outlet-side tube section 12 are aligned with each otherand with an imaginary longitudinal axis L and are advantageously ofone-piece construction, so that they can be fabricated from a singletubular semifinished product, for example; if necessary, however, flowtube 10 and tube sections 11, 12 can also be made from separatesemifinished products that are subsequently joined together, forinstance welded together. For flow tube 10, virtually any of thematerials commonly used for such transducers, such as steel, titanium,zirconium, etc, can be used.

[0069] If the transducer is to be detachable from the pipe, a firstflange 13 and a second flange 14 are preferably formed on inlet-tubesection 11 and outlet-side tube section 12, respectively; if necessary,inlet- and outlet-side tube sections 11, 12 may also be connected withthe pipe directly, for instance by welding or brazing.

[0070] Furthermore, as shown schematically in FIG. 1, a second supportsystem 30 may be fixed to inlet- and outlet-side tube sections 11, 12;preferably, this second support system may be implemented as atransducer case 30′ that houses the flow tube 10, see FIG. 1.

[0071] In operation, flow tube 10 is excited into flexural vibrations,particularly in the range of a natural resonance frequency, such that inthis so-called useful mode, it deflects essentially according to a firstform of natural vibrations.

[0072] In a preferred embodiment of the invention, flow tube 10 isexcited at a vibration frequency that corresponds as exactly as possibleto a natural resonance frequency of the so-called f1 eigenmode of flowtube 10, i.e., to a symmetrical eigenmode, in which, as shownschematically in FIG. 3, the vibrating, but empty flow tube 10 has asingle antinode. For example, in the case of a flow tube 10 of specialsteel with a nominal diameter of 20 mm, a wall thickness of about 1.2mm, and a length of about 350 mm, the resonance frequency of the f1eigenmode is approximately 850 to 900 Hz.

[0073] When fluid flows through the pipe, so that the mass flow rate mis nonzero, Coriolis forces are induced in the fluid by the flow tube 10vibrating in the manner described above. The Coriolis forces react onflow tube 10, thus causing an additional deformation (not shown) of flowtube 10 according to a second form of natural vibrations, which issuperimposed on the excited useful mode as a coplanar mode. Thisdeformation can be detected using sensor technology. The instantaneousshape of the deformation of flow tube 10, particularly in terms of itsamplitudes, is also dependent on the instantaneous mass flow rate m. Thesecond form of natural vibrations, the so-called Coriolis mode, can be,for instance, the antisymmetric f2 eigenmode, i.e., the mode with twoantinodes, and/or the antisymmetric f4 eigenmode with four antinodes, asis usually the case in such transducers.

[0074] When the useful mode is excited, transverse forces Q₁ areproduced in the vibrating single flow tube 10 by mass accelerationsassociated with the flexural vibrations, as is well known; thus,corresponding laterally directed transverse impulses occur in thetransducer. At a vibration amplitude of approx. 0.03 mm, for example, atransverse force of about 100 N would result for the above-mentionedflow tube of special steel.

[0075] If these transverse forces Q₁ are not counterbalanced, atransverse impulse remains in the transducer. As a result, the flow tube10, mounted via inlet-side tube section 11 and outlet-side tube section12, together with the first support system 20 fixed thereto, will belaterally deflected from the assigned static rest position. Accordingly,the transverse forces Q₁ would at least partly act via inlet-side andoutlet-side tube sections 11, 12 on the connected pipe and thus causethe latter to vibrate as well.

[0076] To minimize such oscillating transverse forces Q₁, acting on thepipe, in a preferred embodiment of the invention, the first supportsystem 20 is implemented as an antivibrator 20′ which vibrates out ofphase with, particularly opposite in phase to, flow tube 10, and whichtherefore is preferably flexible.

[0077] Antivibrator 20′ serves to dynamically balance the transducer fora predetermined fluid density value, for instance a value mostfrequently expected during operation of the transducer or a criticalvalue, to the point that the transverse forces Q₁ produced in thevibrating flow tube 10 are compensated as completely as possible andthat flow tube 10 then practically does not leave its static restposition, cf. FIGS. 3a, 3 b. Accordingly, in operation, antivibrator20′, as shown schematically in FIG. 3b, is also excited into flexuralvibrations that are essentially coplanar with the flexural vibrations offlow tube 10.

[0078] To this end, antivibrator 20′, as shown in FIG. 1, is preferablyimplemented in the form of a tube, particularly a tube that is coaxialwith flow tube 10. If necessary, antivibrator 20′, as also shown in U.S.Pat. No. 5,969,265, EP-A 317,340, or WO-A 00/14485, for example, canalso be implemented as a multipart, composite unit or by means of twoseparate antivibrators fixed to flow tube 10 at the inlet end and outletend, respectively, cf. FIG. 2. Particularly in the latter case, wherethe inner support system 20 is formed by means of an inlet-sideantivibrator and an outlet-side antivibrator, the outer support system30 can also be implemented as a two-part system consisting of aninlet-side subsystem and an outlet-side subsystem, cf. FIG. 2.

[0079] To permit easy tuning of antivibrator 20′ to the aforementioneddensity value and the actually excited vibration mode of flow tube 10,in another preferred embodiment of the invention, discrete first andsecond mass pieces 201, 202 are mounted, preferably detachably, onantivibrator 20′. Mass pieces 201, 202 may be, for example, disksscrewed onto staybolts provided on flow tube 10, or short tube sectionsslipped over the flow tube. Furthermore, a corresponding massdistribution over antivibrator 20′ can be realized by forminglongitudinal or annular grooves, for example. A mass distributionsuitable for the respective application can be easily determined by theperson skilled in the art using the finite element method and/orsuitable calibration measurements, for example. If necessary, more thantwo mass pieces 201, 202 can be used, of course. At this point it shouldbe noted that both support systems 20, 30, but at least the antivibrator20′ and the transducer case 30′, can be retrofitted on an existing pipe,as proposed in WO-A 99/51946 or EP-A 1 150 104, for example.

[0080] To generate mechanical vibrations of flow tube 10, the transducerfurther comprises an excitation system 40, particularly anelectrodynamic system. The excitation system serves to convert electricexcitation energy E_(exc) supplied from control electronics (not shown),for instance with a regulated current and/or a regulated voltage, intoan excitation force F_(exc) that acts on flow tube 10, for example in apulsed manner or harmonically, and elastically deforms the tube in themanner described above. The excitation force F_(exc) may bebidirectional as shown schematically in FIG. 1, or unidirectional, andcan be adjusted in amplitude, for instance by means of a current- and/orvoltage-regulator circuit, and in frequency, for instance by means of aphase-locked loop, in the manner familiar to those skilled in the art.The excitation system can be, for example, a simple solenoid with acylindrical excitation coil that is mounted on antivibrator 20′ andtraversed in operation by a suitable excitation current, and with apermanent magnetic armature that is fixed to the outside of flow tube10, particularly at the midpoint thereof, and rides in the excitationcoil at least in part. Excitation system 40 can also be implemented asan electromagnet or, as shown in WO-A 99/51946, as a seismic exciter,for example.

[0081] To detect vibrations of flow tube 10, a sensor system as iscommonly used for such transducers can be employed, in which the motionsof flow tube 10 are sensed with an inlet-side first sensor 50A and anoutlet-side second sensor 50B and converted into corresponding first andsecond sensor signals S₁ and S₂, respectively, in the manner familiar tothose skilled in the art. Sensors 50A, 50B can be electrodynamicvelocity sensors as shown schematically in FIG. 1, which performrelative vibration measurements, or electrodynamic displacement sensorsor acceleration sensors, for example. In place of electrodynamic sensorsystems, sensor systems using resistive or piezoelectric strain gages oroptoelectronic sensor systems can be employed.

[0082] As repeatedly mentioned, flow tube 10 can also be dynamicallybalanced by means of antivibrator 200 for only a single fluid densityvalue, but for a very narrow fluid density range at best, cf. FIG. 3b.During variations in density ρ, however, flow tube 10 will be laterallydisplaced from its rest position, symbolized in FIG. 3a to 3 d by thelongitudinal axis L, namely at high densities ρ above the aforementionedfluid-density value in the direction of its own vibratory motion, asshown schematically in FIG. 3c, and at low densities ρ below thatfluid-density value in the direction of the vibratory motion of theinner support system 20, which may be implemented as antivibrator 20′,as shown in FIG. 3d.

[0083] To improve the dynamic balance of the transducer, particularlyfor fluids with significantly varying density ρ, the transducer furthercomprises a first cantilever 15, fixed as rigidly as possible toinlet-side tube section 11, and a second cantilever 16, fixed as rigidlyas possible to outlet-side tube section 12 and preferably identical inshape to cantilever 15.

[0084] According to the invention, the two cantilevers 15 and 16, whichare preferably disposed symmetrically with respect to the midline offlow tube 10, serve to dynamically produce bending moments in inlet-sidetube section 11 and outlet-side tube section 12, respectively,particularly near the adjoining flow tube 10, when the vibrating flowtube 10, together with antivibrator 20′ if present, is laterallydisplaced from its static rest position. To this end, cantilever 15 andcantilever 16 are positively and/or nonpositively connected, forinstance welded or clamped on, to an outlet end 11# of inlet-tubesection 11 and an inlet end 12# of outlet-tube section 12, respectively.

[0085] As shown schematically in FIGS. 1 and 2, the two cantilevers 15,16 are so positioned in the transducer, preferably as close as possibleto flow tube 10, that a centroid M₁₅ of cantilever 15 and a centroid M₁₆of cantilever 16 are spaced from, and particularly located in line with,flow tube 10. In this manner, moments of inertia are developed by meansof cantilevers 15, 16 which are applied at the respective fixing points,namely outlet at end 11# and inlet end 12#, eccentrically, i.e., not atthe associated centroids M₁₅, M₁₆. These moments of inertia, in turn,cause cantilevers 15, 16 to oscillate about their respective, nearlystationary centroids M₁₅, M₁₆, thus forcing additional twisting ofoutlet end 11# about an imaginary first axis of rotation D₁₅, which isperpendicular to the lateral displacement motion V of flow tube 10 andto the longitudinal axis L, and of inlet end 12# about an imaginarysecond axis of rotation D₁₆, which is essentially parallel to the first,see FIGS. 3c and 3 d.

[0086] This twisting of outlet end 11#, which is shown enlarged in FIG.4, causes additional bending of at least parts of inlet-side tubesection 11 which is directed opposite to the displacement motion V offlow tube 10 and which corresponds to a uniaxial, transverse-force-freeand, thus, shear-stress-free bending; analogously, outlet-tube section12 is bent in opposite direction to the displacement motion V.

[0087] According to findings of the inventors, this bending ofinlet-side and outlet-side tube sections 11, 12 can be optimized, forinstance by means of computer-assisted simulation calculations or bymeans of experimental measurements, such that the above-mentionedtransverse forces Q₁ in the vibrating flow tube 10 are completely or atleast partially balanced by counterforces Q₂ produced by the bending,such that practically no transverse forces caused by the vibrating flowtube 10 and the possibly likewise vibrating internal support system 20will act on the connected pipe. Any deformations of the connected pipecaused by the resulting bending moments can be easily suppressed bysupport system 30, for instance by a suitably high flexural rigidity ofthe above-mentioned transducer case 30′.

[0088] The invention is also predicated in the surprising recognitionthat through a suitable deformation of inlet-side tube section 11 andoutlet-side tube section 12 independently of instantaneous vibrationamplitudes and/or frequencies of flow tube 10 in the above-mentioneduseful mode, i.e., through a suitable shape of a correspondingdeflection line, a force value and a momentum value per unit lengthalong the longitudinal axis L can be set within the transducer in such away that transverse impulses directed opposite to the transverseimpulses produced in the vibrating flow tube 10 can be produced suchthat the transverse impulses neutralize each other, so that thetransverse forces Q₁ produced by the vibrating flow tube 10 can beessentially balanced by means of transverse forces Q₂ produced by thedeforming inlet-side tube section 11 and the deforming outlet-side tubesection 12.

[0089] In a further preferred embodiment of the invention, cantilever 15is so shaped and attached to flow tube 10 that its centroid M₁₅ islocated essentially in a range of one half the length of inlet-side tubesection 11, and cantilever 16 is so shaped and attached to flow tube 10that its centroid M₁₆ is located essentially in a range of one half thelength of outlet-side tube section 12.

[0090] To develop the moments of inertia, cantilever 15, as shown inFIG. 1, has a cantilever arm 15A on which a cantilever mass 15B isformed remote from outlet end 11#; similarly, cantilever 16 has acantilever arm 16A with a cantilever mass 16B formed thereon remote frominlet end 12#. Cantilever masses 15B and 16B are chosen so as to becapable of twisting in response to a lateral deflection of flow tube 10,and thus of inlet and outlet ends 11# and 12#, respectively, but, intranslatory terms, to remain essentially in the respective static restpositions assigned to them on the basis of the concretemechanogeometrical parameters of cantilevers 15, 16. In a correspondingmanner, the respective centroids M₁₅, M₁₆ of the two cantilevers 15, 16remain essentially in their static rest positions although flow tube 10is laterally displaced from its assigned static rest position; they thusserve as a center for the rotary motions of cantilevers 15, 16, whichcause the above-mentioned bending moments.

[0091] Each of the two cantilevers 15, 16 is preferably clamped at oneend, i.e., they are fixed only to outlet and inlet ends 11# and 12#,respectively, as also shown in FIGS. 1 to 4. To suppress any unwantedvibration modes, however, additional spring and/or damping elements asshown schematically in FIG. 4 may be provided which, fixed to therespective cantilever mass 15B, 16B and to transducer case 30′,stabilize the centroids M₁₅, M₁₆ of cantilevers 15, 16 in theirrespective rest positions.

[0092] Experiments on transducers with the above-mentioned flow tube ofspecial steel have shown, for example, that each of the cantilevermasses 15B, 16B, which should be as inert as possible to any lateraldisplacements, particularly in comparison with flow tube 10, shouldadvantageously be chosen to be about five times as large as the mass offlow tube 10. Surprisingly, however, the two cantilever masses 15B, 16Band their cantilever arms 15A, 16A can be proportioned virtuallyindependently of the vibration frequencies of the vibrating flow tube 10which are expected in operation; it must only be ensured that cantilevermasses 15B are made as heavy as possible, particularly heavier than flowtube 10, and that cantilever arms 15A, 16A, as indicated above, are madeas rigid as possible.

[0093] To permit the cantilever masses to be twisted with as littleresistance as possible, cantilevers 15 and 16 are preferably shaped andfixed to flow tube 10 in such a manner that a quotient of theaforementioned moment of inertia and the respective associatedcantilever mass 15B, 16B is as low as possible. Investigations haveshown that, if flow tube 10 is made of special steel as described above,for example, cantilevers 15 and 16 should be so shaped and fixed toinlet-side tube section 11 and outlet-side tube section, respectively,that the aforementioned quotient is less than 10 ⁻⁴ kg·m²/kg. Thequotient can advantageously be set very accurately by implementingcantilever masses 15B and 16B in the form of elongate prisms orcylinders, symbolized in FIGS. 3a to 3 d and 4 by their respective crosssections, and respectively attaching them via cantilever arms 15A and16A to inlet-side and outlet-side tube sections 11 and 12 in such a waythat respective principal axes of inertia for associated minimumprincipal moments of inertia of cantilever masses 15B and 16B areparallel to the aforementioned axes of rotation D₁₅, D₁₆.

[0094] The aforementioned quotient can also be minimized dynamically asa function of the lateral displacement motions V of flow tube 10. Toaccomplish this, in a further preferred embodiment of the invention,cantilever masses 15B, 16B are at least partially made pliable, forinstance by forming grooves substantially parallel to the axes ofrotation D₁₅, D₁₆, as shown schematically in FIG. 1.

[0095] Furthermore, cantilevers 15 and 16 are preferably designed sothat their arms 15A and 16A have a higher flexural rigidity than, andpreferably at least three times the flexural rigidity of, inlet-side andoutlet-side tube sections 11 and 12, respectively. To this end,cantilever arms 15A, 16A may, for instance, be tubular in form, asalready described for antivibrator 20′; then, they can be fixed toinlet-side and outlet-side tube sections 11 and 12, respectively,coaxially with flow tube 10 and in line with antivibrator 20′, if thelatter is present. In that case, cantilever arms 15A, 16A andantivibrator 20′ can be made in one part from a single tubularsemifinished product or in two parts from two tube halves, for example.The above-described ratio of flexural rigidities can also be set, forexample, by selecting inlet-side and outlet-side tube sections 11, 12 ofsuitable length.

[0096] To the inventors' surprise, however, it turned out that thebending moments for inlet-side tube section 11 and outlet side tubesection 12 can also be developed with sufficient accuracy by means ofcantilever arms 15A, 16A that elastically deform significantly withincertain limits. Cantilever masses 15B, 16B can then be designed to besubject to virtually no twisting, remaining in their assigned restpositions, preferably relatively far from flow tube 10. In theabove-mentioned case where cantilever arms 15A, 16A are tubular, thearms may, for instance, be longitudinally slotted for setting both theirflexural rigidity and the above-mentioned quotient.

[0097] As is readily apparent from the above explanations, thetransducer according to the invention is characterized by a multitude ofpossible settings which enable the person skilled in the art,particularly after specification of external or internal mountingdimensions, to achieve high-quality balancing of transverse forcesdeveloped in flow tube 10 and in antivibrator 20′, if present.

[0098] While the invention has been illustrated and described in detailin the drawings and forgoing description, such illustration anddescription is to be considered as exemplary not restrictive incharacter, it being understood that only exemplary embodiments have beenshown and described and that all changes and modifications that comewithin the spirit and scope of the invention as described herein aredesired to protected.

What is claimed is:
 1. A vibratory transducer for a fluid flowing in apipe, said transducer comprising: a flow tube vibrating in operation,for conducting the fluid, said flow tube communicating with the pipe viaan inlet-side tube section and an outlet-side tube section, and saidvibrating flow tube being, at least temporarily, laterally displacedfrom an assigned static rest position as a result of transverse impulsesoccurring in the transducer; an excitation system for driving the flowtube; a sensor system for sensing vibrations of the flow tube; a firstcantilever, fixed to the inlet-side tube section, for causing bendingmoments that elastically deform the inlet-side tube section; and asecond cantilever, fixed to the outlet-side tube section, for causingbending moments that elastically deform the outlet-side tube section,said bending moments being such that in the deforming inlet-side tubesection and in the deforming outlet-side tube section, impulses areproduced which are directed opposite to the transverse impulses producedin the vibrating flow tube.
 2. A transducer as claimed in claim 1wherein the deforming inlet-side tube section and the deformingoutlet-side tube section bend essentially in an opposite direction tothe lateral displacement of the flow tube.
 3. A transducer as claimed inat least one of the claims 1 and 2 wherein the first cantilever has acantilever arm rigidly fixed to the inlet-side tube section and acantilever mass formed thereon, and wherein the second cantilever has acantilever arm rigidly fixed to the outlet-side tube section and acantilever mass formed thereon.
 4. A vibratory transducer for a fluidflowing in a pipe, said transducer comprising: a flow tube vibratingoperation, for conducting the fluid, said flow tube communicating withthe pipe via an inlet-side tube section and an outlet-side tube section,and said vibrating flow tube being, at least temporarily, laterallydisplaced from an assigned rest position as a result of transverseforces produced in the flow tube; an excitation system for driving theflow tube; a sensor system for sensing vibrations of the flow tube; afirst cantilever for causing bending moments that elastically deform theinlet-side tube section, said first cantilever having a cantilever armrigidly fixed to the inlet-side tube section and a cantilever massformed thereon; and a second cantilever for causing bending moments thatelastically deform the outlet-side tube section, said second cantileverhaving a cantilever arm rigidly fixed to the outlet-side tube sectionand a cantilever mass formed thereon, wherein both the cantilever massof the first cantilever and the cantilever mass of the second cantileverbeing spaced from the flow tube, from the inlet-side tube section, andfrom the outlet-side tube section, and the cantilever arm and cantilevermass of the first cantilever and the cantilever arm and cantilever massof the second cantilever being so adapted to one another that a centroidof the first cantilever, located in the area of the inlet-side tubesection, and a centroid of the second cantilever, located in the area ofthe outlet-side tube section, remain essentially in a static restposition although the flow tube is laterally displaced from its assignedstatic rest position.
 5. A transducer as claimed in at least one of theclaims 1 to 4 wherein the flow tube is substantially straight.
 6. Atransducer as claimed in at least one of the claims 1 to 5 wherein thevibrating flow tube performs flexural vibrations.
 7. A transducer asclaimed in at least one of the claims 1 to 6 wherein each of the twocantilevers is at least as heavy as the flow tube.
 8. A transducer asclaimed in at least one of the claims 1 to 7 which transducer comprisesan antivibrator fixed to the flow tube on the inlet and outlet sides. 9.A transducer as claimed in claim 8 wherein the antivibrator is tubularin form.
 10. A transducer as claimed in claims 5 and 8 wherein the flowtube is at least partly enclosed by the antivibrator.
 11. A transduceras claimed in claim 10 wherein the flow tube and the antivibrator arecoaxial.
 12. A transducer as claimed in at least one of the claims 8 to11 wherein grooves are formed in the antivibrator.
 13. A transducer asclaimed in at least one of the claims 8 to 12 wherein discrete, firstand second mass pieces are fixed to the antivibrator.
 14. A transduceras claimed in claim 13 wherein the mass pieces fixed to the antivibratorare annular in shape and coaxial with the antivibrator.